Bayesian capture-recapture analysis and model selection allowing for heterogeneity and behavioral effects

Finite mixtures in capture-recapture surveys for modeling residency patterns in marine wildlife populations

This work aims to show how prior knowledge about the structure of a heterogeneous animal population can be leveraged to improve the abundance estimation from capture-recapture survey data. We combine the Open Jolly-Seber model with finite mixtures and propose a parsimonious specification tailored to the residency patterns of the common bottlenose dolphin. We employ a Bayesian framework for our inference, discussing the appropriate choice of priors to mitigate label-switching and nonidentifiability issues, commonly associated with finite mixture models. We conduct a series of simulation experiments to illustrate the competitive advantage of our proposal over less specific alternatives. The proposed approach is applied to data collected on the common bottlenose dolphin population inhabiting the Tiber River estuary (Mediterranean Sea). Our results provide novel insights into this population's size and structure, shedding light on some of the ecological processes governing its dynamics.

A Simulation Study on Increasing Capture Periods in Bayesian Closed Population Capture-Recapture Models with Heterogeneity

Capture-Recapture models are useful in estimating unknown population sizes. A common modeling challenge for closed population models involves modeling unequal animal catchability in each capture period, referred to as animal heterogeneity. Inference about population size N is dependent on the assumed distribution of animal capture probabilities in the population, and that different models can fit a data set equally well but provide contradictory inferences about N. Three common Bayesian Capture-Recapture heterogeneity models are studied with simulated data to study the prevalence of contradictory inferences is in different population sizes with relatively low capture probabilities, specifically at different numbers of capture periods in the study.

Estimation of capture probabilities using generalized estimating equations and mixed effects approaches

Modeling individual heterogeneity in capture probabilities has been one of the most challenging tasks in capture–recapture studies. Heterogeneity in capture probabilities can be modeled as a function of individual covariates, but correlation structure among capture occasions should be taking into account. A proposed generalized estimating equations (GEE) and generalized linear mixed modeling (GLMM) approaches can be used to estimate capture probabilities and population size for capture–recapture closed population models. An example is used for an illustrative application and for comparison with currently used methodology. A simulation study is also conducted to show the performance of the estimation procedures. Our simulation results show that the proposed quasi-likelihood based on GEE approach provides lower SE than partial likelihood based on either generalized linear models (GLM) or GLMM approaches for estimating population size in a closed capture–recapture experiment. Estimator performance is good if a large proportion of individuals are captured. For cases where only a small proportion of individuals are captured, the estimates become unstable, but the GEE approach outperforms the other methods.

Assessing the impact of climate variation on survival in vertebrate populations

The impact of the ongoing rapid climate change on natural systems is a major issue for human societies. An important challenge for ecologists is to identify the climatic factors that drive temporal variation in demographic parameters, and, ultimately, the dynamics of natural populations. The analysis of long-term monitoring data at the individual scale is often the only available approach to estimate reliably demographic parameters of vertebrate populations. We review statistical procedures used in these analyses to study links between climatic factors and survival variation in vertebrate populations. We evaluated the efficiency of various statistical procedures from an analysis of survival in a population of white stork, Ciconia ciconia, a simulation study and a critical review of 78 papers published in the ecological literature. We identified six potential methodological problems: (i) the use of statistical models that are not well-suited to the analysis of long-term monitoring data collected at the individual scale; (ii) low ratios of number of statistical units to number of candidate climatic covariates; (iii) collinearity among candidate climatic covariates; (iv) the use of statistics, to assess statistical support for climatic covariates effects, that deal poorly with unexplained variation in survival; (v) spurious detection of effects due to the co-occurrence of trends in survival and the climatic covariate time series; and (vi) assessment of the magnitude of climatic effects on survival using measures that cannot be compared across case studies. The critical review of the ecological literature revealed that five of these six methodological problems were often poorly tackled. As a consequence we concluded that many of these studies generated hypotheses but only few provided solid evidence for impacts of climatic factors on survival or reliable measures of the magnitude of such impacts. We provide practical advice to solve efficiently most of the methodological problems identified. The only frequent issue that still lacks a straightforward solution was the low ratio of the number of statistical units to the number of candidate climatic covariates. In the perspective of increasing this ratio and therefore of producing more robust analyses of the links between climate and demography, we suggest leads to improve the procedures for designing field protocols and selecting a set of candidate climatic covariates. Finally, we present recent statistical methods with potential interest for assessing the impact of climatic factors on demographic parameters.

A Bayesian hierarchical model for the estimation of two incomplete surveillance data sets

A model-based approach to analyze two incomplete disease surveillance datasets is described. Such data typically consist of case counts, each originating from a specific geographical area. A Bayesian hierarchical model is proposed for estimating the total number of cases with disease while simultaneously adjusting for spatial variation. This approach explicitly accounts for model uncertainty and can make use of covariates.The method is applied to two surveillance datasets maintained by the Centers for Disease Control and Prevention on Rocky Mountain spotted fever (RMSF). An inference is drawn using Markov Chain Monte Carlo simulation techniques in a fully Bayesian framework. The central feature of the model is the ability to calculate and estimate the total number of cases and disease incidence for geographical regions where RMSF is endemic.The information generated by this model could significantly reduce the public health impact of RMSF and other vector-borne zoonoses, as well as other infectious or chronic diseases, by improving knowledge of the spatial distribution of disease risk of public health officials and medical practitioners. More accurate information on populations at high risk would focus attention and resources on specific areas, thereby reducing the morbidity and mortality caused by some of the preventable and treatable diseases.

On the Bayesian estimation of a closed population size in the presence of heterogeneity and model uncertainty

We consider the estimation of the size of a closed population, often of interest for wild animal populations, using a capture-recapture study. The estimate of the total population size can be very sensitive to the choice of model used to fit to the data. We consider a Bayesian approach, in which we consider all eight plausible models initially described by Otis et al. (1978, Wildlife Monographs 62, 1-135) within a single framework, including models containing an individual heterogeneity component. We show how we are able to obtain a model-averaged estimate of the total population, incorporating both parameter and model uncertainty. To illustrate the methodology we initially perform a simulation study and analyze two datasets where the population size is known, before considering a real example relating to a population of dolphins off northeast Scotland.

Flexible random-effects models using Bayesian semi-parametric models: applications to institutional comparisons

Random effects models are used in many applications in medical statistics, including meta-analysis, cluster randomized trials and comparisons of health care providers. This paper provides a tutorial on the practical implementation of a flexible random effects model based on methodology developed in Bayesian non-parametrics literature, and implemented in freely available software. The approach is applied to the problem of hospital comparisons using routine performance data, and among other benefits provides a diagnostic to detect clusters of providers with unusual results, thus avoiding problems caused by masking in traditional parametric approaches. By providing code for Winbugs we hope that the model can be used by applied statisticians working in a wide variety of applications.